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Chapter 2. The kinematic part of the energy balance equation
Chapter 3. Parametrization of source terms and the energy balance in a growing wind sea
Chapter 4. An optimal interpolation scheme for assimilating altimeter data into the WAM model
Chapter 5 Numerical scheme
Chapter 6 The WAM-model software
Chapter 7 Wind-wave interaction at ECMWF
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3.1 Introduction
In this section we will be faced with the task of providing an efficient parametrization of the source terms as they were introduced in Komen et al. (1994) The need for a parametrization is evident when it is realized that both the exact versions of the nonlinear source term and the wind input require, per grid point, a considerable amount of computation time, say 10 seconds, on the fastest computer that is presently available. In practice, a typical one day forecast should be completed in a time span of the order of two minutes, so it is clear that compromises have to be made regarding the functional form of the source terms in the action balance equation. Even optimization of the code representing the source terms by taking as most inner do-loop, a loop over the number of grid points (thus taking optimal advantage of vectorisation) is not of much help here as the gain in efficiency is at most a factor of 10 and as practical applications usually require several thousands of grid points or more. Furthermore, although modern machines have parallel capabilities which result in a considerable speed up, there has been a tendency to use this additional computation power for increases in spatial resolution, angular and frequency resolution rather then introducing more elaborate parametrizations of the source terms. The present version of the ECMWF wave prediction system has a spatial resolution of 55 km while the spectrum is discretized with 24 directions and 30 frequencies.
In Section 3.2 we therefore discuss a parametrization of wind input and dissipation while Section 3.3 is devoted to a discrete-interaction operator parametrization of the nonlinear interactions. The adequacy of the approximation for wind input and nonlinear transfer is discussed as well. Dissipation owing to bottom friction is not discussed here because the details of its parametrization were presented in Komen et al. (1994, chapter II). We merely quote the main result,
 ,
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(3.1) |
where the constant
. The relative merits of this approach were discussed
as well. Finally, in Section 3.4, in which we study the energy balance equation in growing wind sea, the relative importance of the physics source terms will be addressed.
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23.04.2002 |
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